Question

Evaluate the integral of e^(tanx) sec² x dx

Answer 1

Since $(tan x)'=sec^2 x$, use a substitution: $t = tan x$, $dt = sec^2 x dx$

$$\int e^{tan x} sec^2 x dx = \int e^t dt =e^t +C$$

Substitute $t = tan x$ back into result:

$$e^{tan x} +C$$